Option-Adjusted Spread (OAS)

Credit spread after removing the value of embedded options — computed via BDT binomial tree.

OAS is the true credit spread of a bond with embedded options (calls, puts, prepayment). Computed using a Black-Derman-Toy (BDT) binomial interest rate tree: at each node, short rates are lognormal with risk-neutral probability 0.5, calibrated to the zero curve. A constant spread (OAS) is added to every node rate, and backward induction prices the bond with option exercise rules (callable: value capped at call price; putable: floored at put price). Bisection solves for the OAS that matches the market dirty price. For option-free bonds, OAS ≈ Z-Spread (consistency check). For callable bonds, Z-Spread = OAS + option cost — the OAS is lower because the quoted spread includes compensation for call risk that OAS strips out. OAS lets you compare callable and non-callable bonds on equal footing. Lower OAS = lower credit risk.

Formula

V_{node} = \frac{0.5(V_{up} + V_{dn})}{1 + (r_{node} + OAS) \cdot \Delta t}